Question

Find the measure of all the angles of a parallelogram if one angle is 24 degree less than the twice of the smallest angle?

Answer 1

Hint: In this problem we are given a parallelogram with the measure of one angle 24 degree less than the twice of the smallest angle. By using the properties of parallelogram, we can establish the relationship between measurement of angles and hence we can find a solution to our problem.

Complete step-by-step answer:
Mathematics is related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. One of the most important branches of mathematics is geometry. It includes the analysis of figures using simple theorems and results.

According to our problem, we are given that one of the angles of parallelogram is 24 degree less than the twice of the smallest angle.
Let the smallest Angle be x. For a parallelogram the smallest and the largest angles are adjacent angles. Now according to the question the largest angle will be 2 x - 24 in degrees.

By using the property of the sum of adjacent interior angles, the sum total of the angles is 180 degrees.
 $ \begin{align}
  & x{}^\circ +2x{}^\circ -24{}^\circ =180{}^\circ \\
 & \Rightarrow 3x{}^\circ =204{}^\circ \\
 & \Rightarrow x{}^\circ =\dfrac{204}{3}=68{}^\circ \\
\end{align} $

Now, the smallest angle is 68 in degrees. For the largest angle,
 $ \begin{align}
  & 2x{}^\circ -24{}^\circ =2(68){}^\circ -24 \\
 & \Rightarrow 136{}^\circ -24{}^\circ =112{}^\circ \\
\end{align} $

Therefore, the largest angle is 112 in degrees. And, as we know that in a parallelogram two opposite angles are equal so other angles are also evaluated as of the same measurement in degrees.

Note: The key step in solving this problem is the knowledge of geometrical figures, particularly parallelogram. By using some properties and visual observation we can easily identify the measurement of angles with conclusive evidence. These observation skills will enhance the confidence of students.